# IBDP Maths analysis and approaches : IB Style Question Bank with Solution -HL Paper 2

### Paper 2

Instructions to candidates

• Write your session number in the boxes above.
• Do not open this examination paper until instructed to do so.
• A graphic display calculator is required for this paper.
• Section B: answer all questions in the answer booklet provided. Fill in your session number on the front of the answer booklet, and attach it to this examination paper and your cover sheet using the tag provided.
• Unless otherwise stated in the question, all numerical answers should be given exactly or correct to three significant figures.
• A clean copy of the mathematics HL and further mathematics HL formula booklet is required for this paper.
• The maximum mark for this examination paper is [100 marks].
• Time: 120 minutes

### Topic 2: Functions– SL content

• Topic: SL 2.1
• Different forms of the equation of a straight line.
• Lines with gradients m1 and m2
• Parallel lines m1 = m2.
• Perpendicular lines m1 × m2 = − 1.
• Topic: SL 2.2
• Topic: SL 2.3
• Topic: SL 2.4
• Topic: SL 2.5
• Topic: SL 2.6
• The quadratic function f(x) = ax2 + bx + c: its graph, y -intercept (0, c). Axis of symmetry.
• The form f(x) = a(x − p)(x − q), x intercepts (p, 0) and (q, 0).The form f(x) = a (x − h) 2 + k, vertex (h,k).
• Topic: SL 2.7
• Topic: SL 2.8
• The reciprocal function f(x) = 1 x , x ≠ 0: its graph and self-inverse nature.
• The rational function $$f(x)=\frac{{ax + b}}{{cx + d}}$$and its graph. Equations of vertical and horizontal asymptotes.
• Topic: SL 2.9
• Exponential functions and their graphs
• The function $$f(x)=a^x , a>0,f(x)=e^x$$, $$a > 0$$ , and its graph.
• Logarithmic functions and their graphs:
• The function $$f(x)=log_ax,x>0,f(x)=lnx,x>0$$ , and its graph
• Topic: SL 2.10
• Topic SL 2.11
• Transformations of graphs.
• Translations: y = f(x) + b; y = f(x − a).
• Reflections (in both axes): y = − f(x); y = f( − x).
• Vertical stretch with scale factor p: y= p f(x).
• Horizontal stretch with scale factor $$\frac{1}{q}$$: y = f(qx).
• Composite transformations.

### Topic 2: Functions– AHL content

• Topic: AHL 2.12
• Topic: AHL 2.13
• Rational functions of the form
• $$f(x)=(\frac{ax + b}{cx^2 + dx + e}),and \; f(x)=\frac{ax^2 + bx + c}{dx + e}$$
• Topic: AHL 2.14
• Topic: AHL 2.15
• Topic: AHL 2.16